Instabilities in a Two-Dimensional Combustion Model with Free Boundary |
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Authors: | Claude-Michel Brauner Alessandra Lunardi |
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Affiliation: | Mathématiques Appliquées de Bordeaux?Université Bordeaux I?33405 Talence cedex, France?e-mail: brauner@math.u-bordeaux.fr, FR Dipartimento di Matematica?Università di Parma,?Via D'Azeglio 85/A, 43100 Parma, Italy?e-mail: lunardi@prmat.math.unipr.it, IT
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Abstract: | We prove instability of the planar travelling wave solution in a two-dimensional free boundary problem modelling the propagation of near- equidiffusional premixed flames in the whole plane. We reduce the problem to a fixed boundary fully nonlinear parabolic system. The spectrum of the linearized operator contains an interval [0,ω c ], ω c > 0, so we cannot construct backward solutions. We use an argument about stability of dynamical systems in Banach spaces in order to prove pointwise instability of the moving front. (Accepted: January 31, 2000)?Published online August 21, 2000 |
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